I live in the area and have kids and we're always looking for a nice hike. One hike in Zion that my kids love and ask to do in the summer is shelf canyon. It's just past the 1st tunnel, and there is a great desciption here:
http://www.zionnational-park.com/zion-park-trails-pine.htm I might wait until May for that one though. It gets chilly in there even in the hot summer.
In March, the Quail Creek hike at the Red Cliffs Desert Reserve in Leeds is great. There are some moki steps that can be tricky for kids, but they really look worse than they are only because you've got little ones and you've got your dad hat on. They aren't bad and the rope that is up on top helps when you've got a kid on your back.
2x on Pioneer Park... great place to spend an afternoon. Especially if its a bit chilly out. And the ancestor square is close by, with the carousel and water fountains and lawn for playing frisbee.
Also, Jenny's Canyon, or any of the hikes in Snow Canyon.
Let us know how it goes, and how your kids react. I hope you have great weather when you are down.
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